A ball is thrown vertically upward with an initial speed v and reaches a maximum height y1. The same ball is thrown with an initial speed 3v to reach the maximum height y2. What is the correct relationship between y2 and y1?

y2 = 9y1

Explanation:

According to projectile, the formula for calculating maximum height is expressed as;

Maximum height H = u²/2g

If a ball is thrown vertically upward with an initial speed v and reaches a maximum height y1, then

y1 = v²/2g

2g = v²/y1 1

If the same ball is thrown with an initial speed 3v to reach the maximum height y2, hence;

y2 = (3v)²/2g

2g = 9v²/y2 2

Equate 1 and 2

v²/y1 = 9v²/y2

1/y1 = 9/y2

Cross multiply

9y1 = y2

Rearrange

y2 = 9y1

Hence the correct relationship between y2 and y1 is y2 = 9y1

answer: 802.3 kilo joules of energy represents 191.75 kilo calorie of energy.

explanation:

energy released during combustion of one mole methane = 802.3 kilo joules

if 1 kilo joule = 0.239006   kilo calorie

then ,802.3 kilo joule will be = 802.30.239006 kilo calorie

802.3 kilo joule = 191.75 kilo calorie

hence, the energy in kilo calorie is 191.75 kilo calorie.

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s